提出无需可信第三方的联邦学习安全聚合新方案,降低通信开销。
The Capacity of Information-Theoretic Secure Aggregation in Federated Learning
- 通过用户间通信构建密钥,无需可信第三方或预设结构。
- 实现随机性、密钥传输与聚合通信三者最优平衡,理论容量完全确定。
- 可基于迪菲-赫尔曼密钥交换实现,比谷歌方案少用掩码密钥。
安全聚合使服务器在保护更新隐私的前提下聚合用户本地更新。现有信息论方法通常假设由可信第三方提供相关随机密钥,或通过指定分组结构生成密钥,但忽略了建立这些密钥的通信成本。因此,一般密钥分发机制下的基本极限仍未知。本文研究在N个用户下,支持T-共谋的信息论安全聚合问题,采用包含密钥分发和更新聚合两个阶段的一般框架。不同于以往工作,我们通过用户间通信建模密钥分发,并允许任意用户生成的密钥分发机制,从而消除对可信第三方或预设结构的依赖。该模型实现了对安全性随机性、密钥分发通信量和聚合通信量三者的联合表征。通过构造新颖的安全聚合方案并建立匹配的信息论反证,我们完全刻画了三者之间的容量区域。特别地,我们在任意大小至少为N的有限域上提出了显式确定性容量达成构造,而多数现有方案依赖可信第三方或在足够大的有限域上使用随机或存在性构造。此外,我们证明仅需成对共享密钥即可达到最优性能,可通过迪菲-赫尔曼密钥交换实现。相比谷歌开创性方案,本方案在保持相同聚合通信开销的同时,所需随机掩码密钥更少。
原文摘要 · Abstract (English)
Secure aggregation allows a server to aggregate users' local updates while preserving update privacy. Existing information-theoretic problems typically assume that correlated random keys are provided by a trusted third party (TTP) or generated via prescribed groupwise structures, while the communication cost for establishing such correlated keys is often ignored. Consequently, the fundamental limits under general key-distribution mechanisms remain unknown. In this paper, we study the $T$-colluding information-theoretic secure aggregation problem with $N$ users under a general two-phase framework consisting of a key distribution phase and an update aggregation phase. Unlike prior work, we model key distribution through user-to-user communication and allow arbitrary user-generated key-distribution mechanisms, eliminating TTP or prescribed structures. This enables a joint characterization of three resources: randomness for security, key-distribution communication, and aggregation communication. We completely characterize the capacity region among these three resources by constructing a novel secure aggregation scheme together with a matching information-theoretic converse. In particular, we develop an explicit deterministic capacity-achieving construction over any finite field of size at least $N$, whereas most existing schemes either rely on TTP or employ randomized or existential constructions over sufficiently large finite fields. We further show that the optimal performance can be achieved using only pairwise shared keys, enabling implementation via Diffie--Hellman key exchange. Compared with Google's seminal secure aggregation scheme, the proposed scheme requires fewer random masking keys while preserving the same aggregation communication overhead.
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